Trappistine Abbey in Hakodate City, Hokkaido, is Japan's first female convent, established in 1898 by eight nuns who were dispatched from France. Even today, nuns still live there, so touring the entire convent is not allowed; however, visitors are allowed to freely roam the front garden and one part of the establishment. In the front garden there is a statue of the Archangel Michael, and on a small hill at the end of the path that leads out from the garden is a re-creation of a Catholic pilgrimage site in France called Lourdes Cave. It's a bit of a walk to Lourdes Cave, but there is also an observation deck from which you can look out on Mt. Hakodate, and on clear days you can see as far as Aomori, so it's definitely worth a look.
Additionally, visitors to the abbey will definitely want to buy and bring home madeleines, the French cakes that the nuns make. The cakes have a simple taste reminiscent of long ago, achieved by using a traditional French recipe and no additives. These madeleines can only be purchased from the shop inside the Trappistine Abbey. Because the cakes are made by hand, there is only a limited number of them. It's a popular product that often sells out in the morning, so anyone who wants to try them should plan their visit early.